Question 1

Find the value for the function.
-Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

Accepted Answer

A) $\frac { x ^ { 2 } + 2 x - 6 } { x - 3 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 8 } { x + 5 }$ 
C)  $\frac { x ^ { 2 } - 6 } { x + 5 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 6 } { x + 5 }$ 
A) $\frac { x ^ { 2 } + 2 x - 6 } { x - 3 }$ 
B)  $\frac { x ^ { 2 } + 2 x + 8 } { x + 5 }$ 
C)  $\frac { x ^ { 2 } - 6 } { x + 5 }$ 
D)  $\frac { x ^ { 2 } + 2 x - 6 } { x + 5 }$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\sqrt{x}-5$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Graph the function.
-$$f ( x ) = x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

If y varies directly as x, find a linear function which relates them.
-$$y = 3.6 \text { when } x = 0.9$$

Accepted Answer

A)  $f ( x ) = 4 x$ 
B)  $f ( x ) = 0.25 x$ 
C)  $f ( x ) = x + 2.7$ 
D)  $f ( x ) = 0.9 x$ 
A)  $f ( x ) = 4 x$ 
B)  $f ( x ) = 0.25 x$ 
C)  $f ( x ) = x + 2.7$ 
D)  $f ( x ) = 0.9 x$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{1}{x+5}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
-$$f ( x ) = x ^ { 3 } - 3 x + 3 , ( - 2,2 )$$

Accepted Answer

A)  local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $
decreasing on $ (-1,1) $ 
B)  local maximum at $ (-1,5) $
local minimum at $ (1,1) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
C) local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
D)  local maximum at $( - 1,5 )$
local minimum at $( 1,1 )$
increasing on $( - 1,1 )$
decreasing on $( - 2 , - 1 )$ and $( 1,2 )$ 
A)  local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $
decreasing on $ (-1,1) $ 
B)  local maximum at $ (-1,5) $
local minimum at $ (1,1) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
C) local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
D)  local maximum at $( - 1,5 )$
local minimum at $( 1,1 )$
increasing on $( - 1,1 )$
decreasing on $( - 2 , - 1 )$ and $( 1,2 )$

Question 7

The graph of a function f is given. Use the graph to answer the question.
-What is the domain of $\mathrm { f }$ ?

Accepted Answer

A)  $\{ x \mid x \geq 0 \}$ 
B)  all real numbers 
C)  $\{ x \mid - 4 \leq x \leq 5.5 \}$ 
D)  $\{ x \mid - 5 \leq x \leq 5 \}$ 
A)  $\{ x \mid x \geq 0 \}$ 
B)  all real numbers 
C)  $\{ x \mid - 4 \leq x \leq 5.5 \}$ 
D)  $\{ x \mid - 5 \leq x \leq 5 \}$

Question 8

Find the value for the function.
-Find $- f ( x )$ when $f ( x ) = 2 x ^ { 2 } + 4 x - 4$

Accepted Answer

A)  $2 x ^ { 2 } - 4 x - 4$ 
B)  $- 2 x ^ { 2 } - 4 x + 4$ 
C)  $2 x ^ { 2 } - 4 x + 4$ 
D)  $- 2 x ^ { 2 } - 4 x - 4$ 
A)  $2 x ^ { 2 } - 4 x - 4$ 
B)  $- 2 x ^ { 2 } - 4 x + 4$ 
C)  $2 x ^ { 2 } - 4 x + 4$ 
D)  $- 2 x ^ { 2 } - 4 x - 4$

Question 9

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = 5 x ^ { 3 }$$

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 10

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$$
Find $\frac { f } { g }$

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ x \mid x \neq - \frac { 5 } { 2 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 1 } { 2 \mathrm { x } + 5 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 5 } { 2 } \right\}$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 2 x + 5 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ x \mid x \neq - \frac { 5 } { 2 } \right\}$ 
C)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 1 } { 2 \mathrm { x } + 5 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 5 } { 2 } \right\}$ 
D)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 2 x + 5 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

Question 11

Locate any intercepts of the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
- 5 x + 7 & \text { if } x < 1 \
7 x - 5 & \text { if } x \geq 1
\end{array} \right.$$

Accepted Answer

A)  $( 0 , - 5 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
B)  $( 0,7 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
C)  $( 0 , - 5 )$ 
D)  $( 0,7 )$ 
A)  $( 0 , - 5 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
B)  $( 0,7 ) , \left( \frac { 7 } { 5 } , 0 \right) , \left( \frac { 5 } { 7 } , 0 \right)$ 
C)  $( 0 , - 5 )$ 
D)  $( 0,7 )$

Question 12

Determine whether the equation defines y as a function of x.
-$$y ^ { 2 } = 8 - x ^ { 2 }$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 13

Answer the question about the given function.
-Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$, list the $y$-intercept, if there is one, of the graph of $f$.

Accepted Answer

A)  7 
B)  $- 3$ 
C)  12 
D)  $- 8$ 
A)  7 
B)  $- 3$ 
C)  12 
D)  $- 8$

Question 14

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  square function 
B)  reciprocal function 
C)  linear function 
D)  absolute value function 
A)  square function 
B)  reciprocal function 
C)  linear function 
D)  absolute value function

Question 15

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{1}{4}|x|$.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if
any, and any symmetry with respect to the x-axis, the y-axis, or the origin.
-

Accepted Answer

A) 
function
domain: all real numbers
range: $ \{y \mid y \leq-2 $ or $ y \geq 2\} $
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{y} $-axis 
B) 
function
domain: $ \{x \mid-2 \leq x \leq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ x $-axis, $ y $-axis 
C) 
function
domain: $ \{x \mid x \leq-2 $ or $ x \geq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis, origin 
D) 
$\text { not a function }$ 
A) 
function
domain: all real numbers
range: $ \{y \mid y \leq-2 $ or $ y \geq 2\} $
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{y} $-axis 
B) 
function
domain: $ \{x \mid-2 \leq x \leq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ x $-axis, $ y $-axis 
C) 
function
domain: $ \{x \mid x \leq-2 $ or $ x \geq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis, origin 
D) 
$\text { not a function }$

Question 17

Match the correct function to the graph.
-

Accepted Answer

A)  $y = - 2 x ^ { 2 } + 1$ 
B)  $y = - 2 x ^ { 2 } - 1$ 
C)  $y = 1 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$ 
A)  $y = - 2 x ^ { 2 } + 1$ 
B)  $y = - 2 x ^ { 2 } - 1$ 
C)  $y = 1 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$

Question 18

The graph of a function f is given. Use the graph to answer the question.
-Find the numbers, if any, at which f has a local minimum. What are the local minima?

Accepted Answer

A)  $\mathrm { f }$ has a local minimum at $\mathrm { x } = - \pi$; the local minimum is $- 1$ 
B)  $f$ has a local minimum at $x = 0$; the local minimum is 1 
C)  $f$ has a local minimum at $x = - \pi$ and $\pi$; the local minimum is $- 1$ 
D)  f has no local minimum 
A)  $\mathrm { f }$ has a local minimum at $\mathrm { x } = - \pi$; the local minimum is $- 1$ 
B)  $f$ has a local minimum at $x = 0$; the local minimum is 1 
C)  $f$ has a local minimum at $x = - \pi$ and $\pi$; the local minimum is $- 1$ 
D)  f has no local minimum

Question 19

Solve the problem.
-$$f ( x ) = x ^ { 2 } + 3 x + 7$$

Accepted Answer

A)  $2 \mathrm { x } + \mathrm { h } + 3$ 
B)  1 
C)  $2 x + h + 7$ 
D)  $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 14 } { h }$ 
A)  $2 \mathrm { x } + \mathrm { h } + 3$ 
B)  1 
C)  $2 x + h + 7$ 
D)  $\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h + 14 } { h }$

Question 20

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$(-2,0)$

Accepted Answer

A)  constant 
B)  increasing 
C)  decreasing 
A)  constant 
B)  increasing 
C)  decreasing

Find the value for the function. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

Graph the function. - $f ( x ) = x$

If y varies directly as x, find a linear function which relates them. - $y = 3.6 \text { when } x = 0.9$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 3 x + 3 , ( - 2,2 )$

The graph of a function f is given. Use the graph to answer the question. -What is the domain of $\mathrm { f }$ ? $The graph of a function f is given. Use the graph to answer the question. -What is the domain of \mathrm { f } ?$

Find the value for the function. -Find $- f ( x )$ when $f ( x ) = 2 x ^ { 2 } + 4 x - 4$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 3 }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$ Find $\frac { f } { g }$

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } = 8 - x ^ { 2 }$

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Match the graph to the function listed whose graph most resembles the one given. -

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Match the correct function to the graph. -

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

Solve the problem. - $f ( x ) = x ^ { 2 } + 3 x + 7$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-2,0)$

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

Find the value for the function. -Find f(x+1)f ( x + 1 )f(x+1) when f(x)=x2−7x+4f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }f(x)=x+4x2−7​

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x−5f(x)=\sqrt{x}-5f(x)=x​−5

Graph the function. - f(x)=xf ( x ) = xf(x)=x

If y varies directly as x, find a linear function which relates them. - y=3.6 when x=0.9y = 3.6 \text { when } x = 0.9y=3.6 when x=0.9

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=1x+5f(x)=\frac{1}{x+5}f(x)=x+51​

The graph of a function f is given. Use the graph to answer the question. -What is the domain of f\mathrm { f }f ?

Find the value for the function. -Find −f(x)- f ( x )−f(x) when f(x)=2x2+4x−4f ( x ) = 2 x ^ { 2 } + 4 x - 4f(x)=2x2+4x−4

Determine algebraically whether the function is even, odd, or neither. - f(x)=5x3f ( x ) = 5 x ^ { 3 }f(x)=5x3

For the given functions f and g, find the requested function and state its domain. - f(x)=2x+5;g(x)=6x−1f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1f(x)=2x+5;g(x)=6x−1 Find fg\frac { f } { g }gf​

Locate any intercepts of the function. - f(x)={−5x+7 if x<17x−5 if x≥1f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.f(x)={−5x+77x−5​ if x<1 if x≥1​

Determine whether the equation defines y as a function of x. - y2=8−x2y ^ { 2 } = 8 - x ^ { 2 }y2=8−x2

Answer the question about the given function. -Given the function f(x)=−5x2+10x+7f ( x ) = - 5 x ^ { 2 } + 10 x + 7f(x)=−5x2+10x+7 , list the yyy -intercept, if there is one, of the graph of fff .

Match the graph to the function listed whose graph most resembles the one given. -

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=14∣x∣f(x)=\frac{1}{4}|x|f(x)=41​∣x∣ .

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Match the correct function to the graph. -

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

Solve the problem. - f(x)=x2+3x+7f ( x ) = x ^ { 2 } + 3 x + 7f(x)=x2+3x+7

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−2,0)(-2,0)(−2,0)

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Find the value for the function. -Find $f ( x + 1 )$ when $f ( x ) = \frac { x ^ { 2 } - 7 } { x + 4 }$

Graph the function. - $f ( x ) = x$

If y varies directly as x, find a linear function which relates them. - $y = 3.6 \text { when } x = 0.9$

The graph of a function f is given. Use the graph to answer the question. -What is the domain of $\mathrm { f }$ ? $The graph of a function f is given. Use the graph to answer the question. -What is the domain of \mathrm { f } ?$

Find the value for the function. -Find $- f ( x )$ when $f ( x ) = 2 x ^ { 2 } + 4 x - 4$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 3 }$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$ Find $\frac { f } { g }$

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } - 5 x + 7 & \text { if } x < 1 \\7 x - 5 & \text { if } x \geq 1\end{array} \right.$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } = 8 - x ^ { 2 }$

Answer the question about the given function. -Given the function $f ( x ) = - 5 x ^ { 2 } + 10 x + 7$ , list the $y$ -intercept, if there is one, of the graph of $f$ .

Solve the problem. - $f ( x ) = x ^ { 2 } + 3 x + 7$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $(-2,0)$